3GPP LTE (Long Term Evolution) is a radio access technology for packet-switched services. It is characterized by lack of dedicated channels, and all data in downlink and uplink is transmitted in shared channels. This means that each user (UE, User Equipment) needs to be scheduled in time and frequency in order to be able to receive and transmit data.
The physical layer is based on OFDM (Orthogonal Frequency Division Multiplexing) in both downlink and uplink. One OFDM symbol consists of a number of subcarriers in the frequency domain, depending on the channel bandwidth. One subcarrier in one OFDM symbol can carry one modulation symbol. For data, one UE is always allocated a number of subcarriers in a number of subsequent OFDM symbols.
The scheduling node in LTE is eNodeB (evolved Node B), also called RBS (Radio Base Station).
In uplink, a number of physical channels and physical signals are defined:                PUSCH (Physical uplink shared channel)                    This channel carries data and control, and is shared between all UEs in the cell.                        PUCCH (Physical uplink control channel)                    This channel carries control only and is UE-specific.                        PRACH (Physical random access channel)                    This channel is used by UEs that are not synchronized and which need to access the eNodeB.                        Demodulation reference signals                    These are UE-specific reference signals (pilots) associated with PUSCH or PUCCH, used by eNodeB for channel estimation of PUSCH or PUCCH.                        Sounding reference signals                    These are UE-specific reference signals (pilots) not associated with PUSCH or PUCCH, used by eNodeB for a wideband frequency selective estimate of the channel.                        
The uplink carrier can be viewed as a resource grid with OFDM symbols (also called SC-FDMA symbols, where SC-FDMA is an acronym of Single Carrier Frequency Division Multiple Access and is used to emphasize that all subcarriers used by one UE need to be adjacent) in the time domain and subcarriers in the frequency domain. One RE (resource element) is defined as one OFDM symbol times one subcarrier and can be used to carry one modulation symbol.
The conventional uplink resource grid is illustrated in FIG. 1.
The solid thick rectangle 1 in FIG. 1 denotes an RB (resource block), and the dashed thick rectangle 2 denotes an SB (scheduling block). The size of an RB is one slot (0.5 ms) times 12 subcarriers. RBs can be allocated to either of PUSCH (including demodulation reference signals), PUCCH (including demodulation reference signals) or PRACH. An exception is sounding reference signals that occupy one OFDM symbol in some slots, thus reducing the number of REs for PUSCH.
In FIG. 1, solid empty square denotes PUSCH, left dashed square denote demodulation reference signals for PUSCH, right dashed square denote sounding reference signals and solid gray square denote PRACH. This is just an example of allocating RBs to channels.
It is the task of the uplink scheduler in the RBS to allocate PUSCH SBs to different UEs. It is also a task of the uplink scheduler to select modulation scheme and coding rate per UE. This is of course LTE-specific. In the general case, the scheduler allocates resources per UE, where resources could be frequency, antennas, codes or maybe something else.
The uplink scheduler needs to take (amongst others) the following into account when performing scheduling:                The number of UEs possible to multiplex in the same subframe is limited due to control channel resources in the downlink.        The UEs may have limited amount of data in their transmission buffers. It is a waste to allocate a larger transmission bandwidth than corresponds to the amount of data in the buffer.        The UEs may have a limited capability in terms of amount of data per subframe, limited by the UE category.        The UE has a limited amount of power. The power control mechanism typically strives for keeping the received SINR (signal-to-interference and noise ratio) in the RBS at a constant value. However, when the UE is far from the RBS, or when the path loss is large due to other reasons (in-building penetration loss, shadowing or small-scale fading), the UE power capability may not be enough to keep this target SINR. This also depends on the transmission bandwidth since SINR is proportional to the PSD (power spectral density), which is power per resource unit rather than proportional to the power.        
The transmission is spectral efficient if D/B Number of transmitted bits/bandwidth used for transmission, is maximized. The transmission is power efficient if D/E, Number of transmitted bits/energy used for transmission, is maximized. Wherein:
D=number of transmitted bits
B=bandwidth used for transmission or transmission bandwidth (Hz)
E=energy used for transmission
Spectral efficiency and power efficiency are in conflict with each other. That is since either increased bandwidth or increased energy can be used in order to transmit a certain number of bits.
The upper limit of a channel capacity for an additive white Gaussian noise channel can be calculated according to Shannon's formula:C=B*log2(1+P/(N0*B))where                C: channel capacity (bits/s)        B: transmission bandwidth (Hz)        P: transmission power (W)        N0: noise spectral density (W/Hz)        
It can be seen from the above formula that bandwidth is a more valuable resource than power, since P is inside the logarithmic expression.
In reality, C is limited by the modulation schemes and coding rates supported in the applicable standard, in this example LTE release 8. The most spectral efficient Modulation Coding Scheme (MCS) is given by the highest modulation order and highest coding rate, depending on the implementation of the optional 64QAM capability. It should be noted that LTE release 8 is given as an example and later LTE releases may implement other modulations and code rates.
The most power efficient modulation scheme in LTE release 8 is QPSK. It can be understood that it is more power efficient than 16QAM since the distance between the symbols in the constellation diagram is longer for the same average power. The most efficient coding rate is ⅓ since that is the mother code rate of the Turbo codec. More robust coding can be used by applying repetition, but that does not increase the power efficiency.
The existing straightforward uplink scheduling method, e.g. LTE release 8, comprises the steps of:                List the UEs in priority order. This priority order could be decided by any method and include any criteria such as channel quality, fairness, subscription priority etc.        Decide which UEs to schedule in the current subframe, depending on the amount of available downlink control channel resources.        For each UE, try to schedule as much data as possible. That is, let the data size be limited by the amount of data in buffer, UE capability, UE power or number of remaining SBs.        Optionally, the uplink scheduler can divide the total number of SBs between the selected UEs in the first step, and then adapt the amount of data per UE according to this pre-selected transmission bandwidth.        Select the transport format (modulation scheme and coding rate) so that the quality requirements are met with as little margin as possible, in order to be spectral efficient.        
Thus, the straightforward approach has a number of problems:                If the UE becomes power limited, this is that it needs to reduce the power spectral density if the transmission bandwidth is increased, then the spectral efficiency decreases if more SBs are added, even if this means that more data can be scheduled.        By using the most efficient transport format, UE power consumption is not optimized in cases when not all transmission bandwidth is utilized.        